Relative permeabilities and capillary number correlations are widely used for quantitative estimates of enhanced water flood performance in porous media. They enter as essential parameters into reservoir simulations. Experimental capillary number correlations for seven different reservoir rocks and 21 pairs of wetting and nonwetting fluids are analyzed. The analysis introduces generalized local macroscopic capillary number correlations. It eliminates shortcomings of conventional capillary number correlations. Surprisingly, the use of capillary number correlations on reservoir scales may become inconsistent in the sense that the limits of applicability of the underlying generalized Darcy law are violated. The results show that local macroscopic capillary number correlations can distinguish between rock types. The experimental correlations are ordered systematically using a three-parameter fit function combined with a novel fluid pair based figure of merit.

Sub-Gaussian and subexponential distributions are introduced and applied to study the fluctuation-response relation out of equilibrium. A bound on the difference in expected values of an arbitrary sub-Gaussian or subexponential physical quantity is established in terms of its sub-Gaussian or subexponential norm. Based on that, we find that the entropy difference between two states is bounded by the energy fluctuation in these states. Moreover, we obtain generalized versions of the thermodynamic uncertainty relation in different regimes. Operational issues concerning the application of our results in an experimental setting are also addressed, and nonasymptotic bounds on the errors incurred by using the sample mean instead of the expected value in our fluctuation-response inequalities are derived.

Understanding and modeling the dynamics of multiscale systems is a problem of considerable interest both for theory and applications. For unavoidable practical reasons, in multiscale systems, there is the need to eliminate from the description the fast and small-scale degrees of freedom and thus build effective models for only the slow and large-scale degrees of freedom. When there is a wide scale separation between the degrees of freedom, asymptotic techniques, such as the adiabatic approximation, can be used for devising such effective models, while away from this limit there exist no systematic techniques. Here, we scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to those obtained using multiscale asymptotic techniques and, remarkably, remains effective in predictability also when the scale separation is reduced. We also show that predictability can be improved by hybridizing the reservoir with an imperfect model.

This paper is concerned with the robustness of the sustained oscillations predicted by an epidemic ODE model defined on contact networks. The model incorporates the spread of awareness among individuals and, moreover, a small inflow of imported cases. These cases prevent stochastic extinctions when we simulate the epidemics and, hence, they allow to check whether the average dynamics for the fraction of infected individuals are accurately predicted by the ODE model. Stochastic simulations confirm the existence of sustained oscillations for different types of random networks, with a sharp transition from a nonoscillatory asymptotic regime to a periodic one as the alerting rate of susceptible individuals increases from very small values. This abrupt transition to periodic epidemics of high amplitude is quite accurately predicted by the Hopf-bifurcation curve computed from the ODE model using the alerting rate and the infection transmission rate for aware individuals as tuning parameters.

Both polymer fiber glasses and bulk polymer glasses exhibit nonlinear mechanical responses under uniaxial deformation. In polymer fibers, however, polymer chains are confined strongly and the surface area is relatively large compared to their volume. The confinement and the surface may lead to the spatially heterogeneous relaxation of chains in polymer fibers. In this work we perform molecular dynamics simulations and investigate the relation between the heterogeneous dynamics and the nonlinear mechanical responses at a molecular level. Our molecular simulations capture successfully not only the nonlinear mechanical response but also the dependence of mechanical properties on the strain rate of typical polymer glasses as in experiments. We find that the local elastic modulus and the nonaffine displacement are spatially heterogeneous in the pre-yield regime, which results in a lower elastic modulus for polymer fibers than bulk polymer glasses. In the post-yield regime, those mechanical properties become relatively homogeneous. Monomers with large nonaffine displacement are localized mainly at the interfacial region in the pre-yield regime while highly nonaffine monomers are distributed throughout the fibers in the post-yield regime. We show that the nonaffine displacement during deformation relates closely to the mechanical response of the polymer fibers. We also find that in the strain-hardening regime there is a significant difference in the energetic contribution to the stress between polymer fibers and bulk polymers, for which the modulus of the strain-hardening regime of the polymer fibers is smaller than that of bulk polymers.

Boron carbide (${\mathrm{B}}_4\mathrm{C}$) is of both fundamental scientific and practical interest due to its structural complexity and how it changes upon compression, as well as its many industrial uses and potential for use in inertial confinement fusion (ICF) and high-energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of ${\mathrm{B}}_4\mathrm{C}$ in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of ${\mathrm{B}}_4\mathrm{C}$ over a broad range of temperatures ($\sim 6\times {10}^3$–$5\times {10}^8$ K) and densities (0.025–50 $\mathrm{g}/{\mathrm{cm}}^3$). We assess that the largest discrepancies between theoretical predictions are $\lesssim 5\%$ near the compression maximum at 1–$2\times {10}^6$ K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are $\sim 18\%$ and occur at temperatures between $6\times {10}^3$–$2\times {10}^5$ K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. To account for potential differences in the ion thermal term, we have developed three new equation-of-state models that are consistent with theoretical calculations and experiment. We apply these new models to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.

Betatron radiation generated by relativistic electrons during their wiggling motion in an ion channel is a well-studied source of x-ray photons. Due to the highly collimated emission such compact laser-driven sources have attracted significant attention in various laser or plasma-based applications, but the spectral intensity is still too low. The high repetition rate is also demanded, thus the pulse energy is strongly limited. Here, based on theory and computer simulations, we present a different method to enhance the radiation power by increasing the number of betatron oscillations along the acceleration path of electrons. A stronger wiggling of electrons is achieved by using clusterized gas targets, which allows one to achieve three orders of magnitude higher x-ray yield than in optimized uniform gas target with similar average electron density.

Volume exclusion and single-file diffusion play an important role at very small scales, such as those associated with molecular machines, ion channels, and transport in zeolites, while introducing fundamental differences compared to Brownian motion, such as changes to the power-law relation between the mean square displacement and time. In this work we map the chemical master equation for excluded diffusion onto a Schrödinger equation via annihilation and creation ladder operators with fermionic statistics, together with linear and symbolic algebra with the resulting Fock-space representation to describe the effect of volume-exclusion processes in finite one-dimensional chains. We contrast the dynamics with the nonexclusive (bosonic) diffusion for crowded, intermediate, and dilute particle populations. Motivated by shuttling in molecular machines, we proceed to investigate differences in exit time distributions introduced by volume exclusion, incorporating the presence of transport bias. More generally, this study demonstrates how one can analyze volume-excluded transport for small stochastic systems, without the need for stochastic simulation and ensemble averaging, simply by considering anticommutation relations and fermionic statistics in a Fock-space representation of the stochastic dynamics.

Modeling of random sequential adsorption (RSA) process is studied in this paper as this kind of process is close to the surface adsorption phenomenon that is, for instance, exploited in gas sensors or for liquid or gas purification. Analysis and simulation of the RSA process is first performed to highlight a power-law kinetic behavior. Such behaviors are often modeled in the literature with fractional models. The paper, however, shows that fractional models are not able to capture some important properties of the RSA process. A nonlinear model and the associated parameters tuning method are, thus, proposed. A discussion on the ability of the proposed model to capture the power-law kinetics without exhibiting some of the drawbacks of fractional models is proposed. This nonlinear model is then modified to take into account the reverse desorption process. The proposed modeling approach is applied to experimental data of ${\mathrm{CO}}_2$ capture.

Compared to that for two-dimensional (2D) lattices, our understanding of heat conduction in 2D gases is still limited. Here we study heat conduction behavior of 2D gas systems with momentum-conserving and -nonconserving interparticle interactions by using the nonequilibrium and equilibrium molecular dynamics methods. For the momentum-conserving system, we find that when the dimensionality of the system is changed from 2D to quasi-one-dimensional (quasi-1D), the heat conductivity $\kappa$ diverges with the system size $L$ as $\kappa \sim lnL$ (the theoretical prediction for 2D systems) for a short $L$ and shows, in the thermodynamic limit, a tendency to $\kappa \sim L^{1/3}$ like that predicted in 1D fluids. This suggests that the dimensional-crossover effect of heat conduction exists in 2D systems with conserved momentum. In contrast, for the momentum-nonconserving system, as $L$ increases, finite heat conductivity independent of $L$ is observed. These findings are in agreement with the predictions given by hydrodynamic theory and thus further confirm the validity of the theory in 2D gases.

We demonstrate the emission of solitons from a resonantly excited localized standing wave in a nonlinear chain of spring-coupled masses. The localized wave in this system is induced by a properly designed “impurity” and vibrates around the “impurity” with an intrinsic frequency. We observe that, when subjected to an external forcing, it is amplified to a large amplitude under the nonlinear resonance, and, then, its wave envelope splits apart leading to the release of most of its energy in the form of a large-amplitude traveling soliton. The experiment also shows that the rate of the emission can be controlled by finely tuning the driving parameters, thereby providing a feasible and controllable way for creation of solitons.

It is known that the leaky integrate-and-fire neural model shows a transition from irregular to synchronous firing by increasing the coupling between the neurons. However, a quantitative characterization of this order-disorder transition, that is, the determination of the order of transition and also the critical exponents in the case of continuous transition, is not entirely known. In this work, we consider a network of $N$ excitatory neurons with local connections, residing on a square lattice with periodic boundary conditions. The cooperation between neurons $K$ plays the role of the control parameter that generates criticality when the critical cooperation strength $K_c$ is adopted. We introduce the population-averaged voltage (PAV) as a representative value of the network's cooperative activity. Then, we show that the coupling between the timing of spikes and the phase of temporal fluctuations of PAV defined as $m$ resorts to identify a Kuramoto order parameter. By increasing $K$, we find a continuous transition from irregular spiking to a phase-locked state at the critical point $K_c$. We deploy the finite-size scaling analysis to calculate the critical exponents of this transition. To explore the formal indicator of criticality, we study the neuronal avalanches profile at this critical point and find a scaling behavior with the exponents in a fair agreement with the experimental values both in vivo and in vitro.

The movement of spherical Brownian particle carried by an alternating fluid flow in a tube of periodically variable diameter is investigated. On the basis of our previous results [Phys. Rev. E 99, 012604 (2019)] on the hydrodynamics of the problem, we look at the competition of hydrodynamics and diffusion. We use the method of Fick-Jacobs mapping on an effective one-dimensional problem. We calculate the ratchet current and show that is is strictly related to finite size of the particles. The ratchet current grows quadratically with particle radius. We also show that the dominant contribution to the ratchet current is due to inertial hydrodynamic effects. This means that Reynolds number must be at least of order one. We discuss the possible use for separation of particles by size and perspectives of optimization of the tube shape.

The phase behavior of supersoft spheres is explored using solutions of ultralow cross-linked poly(N-isopropylacrylamide)-based microgels as a model system. For these microgels, the effects of the electric charges on their surfaces can be neglected and therefore only the role of softness on the phase behavior is investigated. The samples show a liquid-to-crystal transition at higher volume fraction with respect to both hard spheres and stiffer microgels. Furthermore, stable body centered cubic (bcc) crystals are observed in addition to the expected face centered cubic (fcc) crystals. Small-angle x-ray and neutron scattering with contrast variation allow the characterization of both the microgel-to-microgel distance and the architecture of single microgels in crowded solutions. The measurements reveal that the stable bcc crystals depend on the interplay between the collapse and the interpenetration of the external shell of the ultralow cross-linked microgels.

An alluvial river builds its own bed with the sediment it transports; its shape thus depends not only on its water discharge but also on the sediment supply. Here we investigate the influence of the latter in laboratory experiments. We find that, as their natural counterpart, laboratory rivers widen to accommodate an increase of sediment supply. By tracking individual particles as they travel downstream, we show that, at equilibrium, the river shapes its channel so that the intensity of sediment transport follows a Boltzmann distribution. This mechanism selects a well-defined width over which the river transports sediment, while the sediment remains virtually idle on its banks. For lack of a comprehensive theory, we represent this behavior with a single-parameter empirical model which accords with our observations.

We investigate with a linear analysis the stability of a horizontal liquid layer subjected to injection of gas bubbles through a bottom wall. The injection is assumed uniform in space and constant in time. Injected bubbles ascend in the liquid layer due to the Archimedean buoyancy force and are ejected from the top free surface of the liquid layer. Modeling this two-phase flow system as two interpenetrating liquid and gas continua, we show that homogeneous upward gas flows become unstable at large gas fluxes. We determine the critical conditions of this homogeneous-heterogeneous regime transition and show that the critical modes are made of stationary convection rolls, either multi- or whole-layered depending on liquid viscosity, the radius of bubbles, and the thickness of liquid layer. By examining the energy transfer from base to perturbation flows, we indicate that liquid convective motion is driven by the buoyancy on heterogeneously distributed bubbles. We also reveal that the lift forces on bubbles have significant stabilizing effects by homogenizing bubble distribution close to the bottom wall.

We demonstrate through experiments and numerical simulations that low-density, low-loss, meter-scale plasma channels can be generated by employing a conditioning laser pulse to ionize the neutral gas collar surrounding a hydrodynamic optical-field-ionized (HOFI) plasma channel. We use particle-in-cell simulations to show that the leading edge of the conditioning pulse ionizes the neutral gas collar to generate a deep, low-loss plasma channel which guides the bulk of the conditioning pulse itself as well as any subsequently injected pulses. In proof-of-principle experiments, we generate conditioned HOFI (CHOFI) waveguides with axial electron densities of $n_{\mathrm{e}0}\approx 1\times {10}^{17}{\mathrm{cm}}^{-3}$ and a matched spot size of $26\mu \mathrm{m}$. The power attenuation length of these CHOFI channels was calculated to be $L_{\mathrm{att}}=(21\pm 3)\mathrm{m}$, more than two orders of magnitude longer than achieved by HOFI channels. Hydrodynamic and particle-in-cell simulations demonstrate that meter-scale CHOFI waveguides with attenuation lengths exceeding 1 m could be generated with a total laser pulse energy of only 1.2 J per meter of channel. The properties of CHOFI channels are ideally suited to many applications in high-intensity light-matter interactions, including multi-GeV plasma accelerator stages operating at high pulse repetition rates.